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Keywords:

  • cyclic graph decompositions;
  • labelings of tripartite graphs

Abstract

We introduce two new labelings for tripartite graphs and show that if a graph G with n edges admits either of these labelings, then there exists a cyclic G-decomposition of inline image for every positive integer x. We also show that if G is the union of two vertext-disjoint cycles of odd length, other than inline image, then G admits one of these labelings.